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1.
Limit theorems for inverse process <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> of Hawkes process
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Youngsoo Seol 《数学学报(英文版)》2017,33(1):51-60
We consider linear Hawkes process N t and its inverse process T n . The limit theorems for N t are well known and studied by many authors. In this paper, we study the limit theorems for T n . In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for T n . The main tool of the proof is based on immigration-birth representation and the observations on the relation between N t and T n . 相似文献
2.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
3.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
4.
Vladimir V. Tkachuk 《Acta Mathematica Hungarica》2005,107(4):253-265
Summary We prove that, for any Tychonoff X, the space Cp(X) is K-analytic if and only if it has a compact cover {Kp: p } such that Kp subset Kq whenever p,q and p q. Applying this result we show that if Cp(X) is K-analytic then Cp(X) is K-analytic as well. We also establish that a space Cp(X) is K-analytic and Baire if and only if X is countable and discrete. 相似文献
5.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
6.
S. B. Yakubovich 《Lithuanian Mathematical Journal》2005,45(1):102-122
We establish the boundedness properties in L
p
for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in L
p
(R
+), 1 p 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 127–147, January–March, 2005. 相似文献
7.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
8.
Perturbative Test of Single Parameter Scaling for 1<Emphasis Type="Italic">D</Emphasis> Random Media
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single parameter scaling holds to lowest order perturbation theory in the disorder strength. However, it is generically violated at higher order. This is explicitly exhibited for the Anderson model.Communicated by Yosi Avronsubmitted 15/03/04, accepted 23/04/04 相似文献
9.
V. M. Kaplitskiĭ 《Siberian Mathematical Journal》2010,51(2):255-266
We show that Peetre’s classical interpolation theorem in weighted L
p
-spaces is carried over to some classes of nonlinear operators containing in particular the Lipschitz operators and operators
close to them in the properties satisfying less restrictive conditions than Lipschitz in each of the spaces of a Banach pair. 相似文献
10.
Yan QU 《数学学报(英文版)》2007,23(10):1903-1908
Let π be an irreducible unitary cuspidal representation of GLm(AQ) with m ≥ 2, and L(s, Tr) the L-function attached to π. Under the Generalized Riemann Hypothesis for L(s,π), we estimate the normal density of primes in short intervals for the automorphic L-function L(s, π). Our result generalizes the corresponding theorem of Selberg for the Riemann zeta-function. 相似文献
11.
C. Pollett 《Journal of Mathematical Sciences》2005,130(2):4607-4619
The notion of a uniform sequent-calculus proof is introduced. It is shown that a strengthening, Sk,exp
, of the well-studied bounded arithmetic system Sk of Buss does not prove NP = co-NP with a uniform proof. A slightly stronger result that Sk,exp
cannot prove
uniformly for 2 ≤ k′ ≤ k is also established. A modification of the technique used is applied to show that Sk,exp
is unable to prove the Davis-Putnam-Robinson-Matiyasevich theorem. Generalizations of these results to higher levels of the Grzegorczyck hierarchy are presented. Bibliography: 21 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 304, 2003, pp. 99–120. 相似文献
12.
Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play
a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with A
0 = A
1
A
1 and dim A
1 = 2 are of type N and give a class of Novikov superalgebras of type S with A
0 = A
1
A
1. 相似文献
13.
Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L
p
-space L
p
(G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L
p
(G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L
p
(G, ω) is a Banach algebra, then G is σ-compact. 相似文献
14.
In this paper we examine the classes of graphs whose Kn-complements are trees or quasi-threshold graphs and derive formulas for their number of spanning trees; for a subgraph H of Kn, the Kn-complement of H is the graph Kn–H which is obtained from Kn by removing the edges of H. Our proofs are based on the complement spanning-tree matrix theorem, which expresses the number of spanning trees of a graph as a function of the determinant of a matrix that can be easily constructed from the adjacency relation of the graph. Our results generalize previous results and extend the family of graphs of the form Kn–H admitting formulas for the number of their spanning trees.Final version received: March 18, 2004 相似文献
15.
W.-D. Richter 《Lithuanian Mathematical Journal》2009,49(1):93-108
For p > 0, the l
n,p
-generalized surface measure on the l
n,p
-unit sphere is studied and used for deriving a geometric measure representation for l
n,p
-symmetric distributions having a density. 相似文献
16.
In previous papers, we have constructed and studied mappings d
k
: M × M → ℝ called the H
k
-distance functions. The main result of this paper is a theorem on realizability of the generalized distances d
k
(υ, w), υ, w ∈ M, by critical values of the length functional L: Ω(M, υ, w) → ℝ generated by nontrivial homology classes of the space Ω(M, υ, w) of paths joining the points υ and w. 相似文献
17.
In this paper we study the L
p
-discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which
is also known as Roth net) with N points has L
p
-discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has L
p
-discrepancy (p an even integer) of order
which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L
2-discrepancy of digitally shifted Hammersley point sets which show that the value of the L
2-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position
of these.
This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305. 相似文献
18.
V. O. Pekhterev 《Ukrainian Mathematical Journal》2009,61(9):1467-1474
We study the structure of the semigroup OT
n
, which is a unique (up to an isomorphism) R-section of the semigroup T
n
. For this semigroup, we describe Green relations, determine regular and nilpotent elements, describe maximal nilpotent subsemigroups,
and determine the unique irreducible system of generatrices and maximal subsemigroups. 相似文献
19.
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D
* is an FC-group, then D is a field. Let M be a maximal subgroup of GL
n
(D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M
n
(D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞. 相似文献
20.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献